Question: Express this quotient in scientific notation: ${\frac{1.500\times 10^{-4}} {5.0\times 10^{-1}}}$
Solution: Start by collecting like terms together. $= {\frac{1.500} {5.0}} \times{\frac{10^{-4}} {10^{-1}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.30 \times 10^{-4\,-\,-1}$ $= 0.30 \times 10^{-3}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.30$ is the same as $3.00 \div 10$ , or $3.00 \times 10^{-1}$ $ = {3.00 \times 10^{-1}} \times 10^{-3} $ $= 3.00\times 10^{-4}$